50.24.4 problem 7(a)

Internal problem ID [8170]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 7. Laplace Transforms. Section 7.5 The Unit Step and Impulse Functions. Page 303
Problem number : 7(a)
Date solved : Sunday, March 30, 2025 at 12:47:16 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} L i^{\prime }+R i&=E_{0} \operatorname {Heaviside}\left (t \right ) \end{align*}

Using Laplace method With initial conditions

\begin{align*} i \left (0\right )&=0 \end{align*}

✓ Maple. Time used: 0.080 (sec). Leaf size: 21

ode:=L*diff(i(t),t)+R*i(t) = E__0*Heaviside(t); 
ic:=i(0) = 0; 
dsolve([ode,ic],i(t),method='laplace');
 

\[ i = \frac {E_{0} \left (1-{\mathrm e}^{-\frac {R t}{L}}\right )}{R} \]

✓ Mathematica. Time used: 0.071 (sec). Leaf size: 25

ode=L*D[i[t],t]+R*i[t]==E0*UnitStep[t]; 
ic={i[0]==0}; 
DSolve[{ode,ic},i[t],t,IncludeSingularSolutions->True]
 

\[ i(t)\to \frac {\text {E0} \theta (t) \left (1-e^{-\frac {R t}{L}}\right )}{R} \]

✗ Sympy

from sympy import * 
t = symbols("t") 
E__0 = symbols("E__0") 
L = symbols("L") 
R = symbols("R") 
i = Function("i") 
ode = Eq(-E__0*Heaviside(t) + L*Derivative(i(t), t) + R*i(t),0) 
ics = {i(0): 0} 
dsolve(ode,func=i(t),ics=ics)
 

ValueError : Couldnt solve for initial conditions